In Exercises 11–22, estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than 10^-4 by (a) the Trapezoidal Rule (The integrals in Exercises 11–18 are the integrals from Exercises 1–8.)
∫ from -1 to 1 of (t³ + 1) dt

Lifetime of a tire Assume the random variable L in Example 2f is normally distributed with mean μ = 22,000 miles and σ = 4,000 miles.

a. In a batch of 4000 tires, how many can be expected to last for at least 18,000 miles?

81. Find the values of p for which each integral converges.

a. ∫ from 1 to 2 of [dx / (x (ln x)^p)]

In Exercises 11–22, estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than 10^-4 by (a) the Trapezoidal Rule (The integrals in Exercises 11–18 are the integrals from Exercises 1–8.)

∫ from 1 to 2 of 1/s² ds

Finding area

Find the area of the region enclosed by the curve y = x cos(x) and the x-axis (see the accompanying figure) for:

a. π/2 ≤ x ≤ 3π/2.

Finding volume: Find the volume of the solid generated by revolving the region bounded by the x-axis and the curve y = x sin(x), 0 ≤ x ≤ π, about

a. The y-axis.

(See Exercise 57 for a graph.)

Evaluate ∫ sec θ dθ by:

a. Multiplying by (sec θ + tan θ) / (sec θ + tan θ) and then using a u-substitution.